10th samacheer kalvi math solution for exercise 5.3 part 2

This page 10th samacheer kalvi math solution for exercise 5.3 part 2 is going to provide you solution for every problems that you find in the exercise no 5.3

10th samacheer kalvi solution for exercise 5.3 part 2

4. Find the angle of inclination of the line passing through the points

(i) (1, 2) and (2 , 3)

Solution:

x₁ = 1 x₂ = 2

y₁ = 2 y₂ = 3

(y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁)

(y - 2)/(3 - 2) = (x - 1)/(2 - 1)

(y - 2)/1 = (x - 1)/1

y - 2 = x - 1

x - y - 1 + 2 = 0

x - y + 1 = 0

(ii) (3 , 3) and (0 , 0)

x₁ = 3 x₂ = 0

y₁ = 3 y₂ = 0

(y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁)

(y - 3)/(0 - 3) = (x - 3)/(0 - 3)

(y - 3)/(-3) = (x - 3)/(-3)

- 3 (y - 3) = -3 (x - 3)

- 3 y + 9 = - 3 x + 9

3 x - 3 y + 9 - 9 = 0

3 x - 3 y = 0

divide the whole equation by 3

x - y = 0

(iii) (a , b) and (-a , -b)

x₁ = a x₂ = -a

y₁ = b y₂ = -b

(y-y₁)/(y₂-y₁) = (x-x₁)/(x₂-x₁)

(y - b)/(-b - b) = (x - a)/(-a - a)

(y - b)/(-2b) = (x - a)/(-2a)

- 2a (y - b) = -2b (x - a)

-a y + ab = -b x + ab

b x - a y + ab - ab = 0

b x - a y = 0

5. Find the slope of the line which passes through the origin and the midpoint ofthe line segment joining the points (0 ,- 4) and (8 , 0).

Solution:

midpoint of the line segment joining the points (0,-4) and (8 , 0)

midpoint =(x₁ + x₂)/2 , (y₁ + y₂)/2

x₁ = 0 x₂ = 8

y₁ = -4 y₂ = 0

= (0 + 8)/2 , (-4 + 0)/2

= 8/2 , -4/2

= (4 , -2)

now we need to find the slope of the line which passes through origin

x₁ = 4 x₂ = 0

y₁ = -2 y₂ = 0

m = (y₂ - y₁)/(x₂ - x₁)

= (0 - (-2))/(0 - 4)

= 2/(-4)

= -1/2

In the page 10th samacheer kalvi math solution for exercise 5.3 part 2 we are going to see the solution of next problem

6. The side AB of a square ABCD is parallel to x-axis . Find the (i) slope of AB (ii) slope of BC (iii) slope of the diagonal AC

Solution:

(i) Since the side AB is parallel to x axis,

slope of the side AB = 0

(ii) The angle formed by the side BC is 90.

m = tan θ

θ = 90

m = tan 90

= ∞

(iii) The diagonal AC is the angle bisector of the angle.

m = tan θ

θ = 45

m = tan 45

= 1

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